双曲映射定轨的渐近性态
Asymptotic behaviour of orbit determination for hyperbolic maps
摘要：
本文研究双曲映射的定轨问题。问题在于确定轨道的初始条件，并最终从一些观测中确定模型的其他参数。我们研究的行为的置信区域的情况下，同时增加的观察和时间跨度，它们被执行。更确切地说，我们描述的几何形状的置信区域的解决方案，区分是否添加参数的估计的初始条件或没有。我们证明，动力学参数的引入会导致不确定性衰减速率的变化，正如一些已知的数值证据所表明的那样。
英文摘要：
We deal with the orbit determination problem for hyperbolic maps. The problem consists in determining the initial conditions of an orbit and, eventually, other parameters of the model from some observations. We study the behaviour of the confidence region in the case of simultaneous increase of the number of observations and the time span over which they are performed. More precisely, we describe the geometry of the confidence region for the solution, distinguishing whether a parameter is added to the estimate of the initial conditions or not. We prove that the inclusion of a dynamical parameter causes a change in the rate of decay of the uncertainties, as suggested by some known numerical evidences.
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